# Normalized regression coefficients - interpratation

I have data containing several variables. I ran a regression model. Prior to running the model I have normalized the dependent variable Y and the independent variables X1 and X2.

After receiving the output I want to interpret the results. For example, if the coefficient of X1 is 0.15, I know that it means that for addition of one standard deviation of X1, there is an increase of 0.15 standard deviations in Y, but this is not clear.

I want to go back to the original units of Y and X for interpretation. How do I do that ? Can I simply take the "normalized coefficients", multiply by the standard deviation of Y and add the mean of Y?

Something about it doesn't make me comfortable.

• Would you please post a link to the raw data? I would like to surface fit "Y = f(X1, X2)"and see what I find with an equation search. – James Phillips Jan 23 '19 at 16:02

Firstly, why did you normalized Y? It will make your output harder to interpret, and it is often not necessary to standardize the dependent variable.

I presume you have centered and scaled you X's, you can backtransform them to interpret,

        # run your model with the X's standardized

mean <- mean(x1)
sd <- sd(x1)

b1*(x1-mean)/sd

#you can also plot

plot(y~x1)


I also recommend to use Y at its original scale, since standardization does not change the distribution shape.

• Can I say that the change in Y is actually the "standardized coefficient" multiplied by the standard deviation of Y ? I think it makes sense – user3275222 Jan 23 '19 at 16:08